Parameter identification for the shallow water equation using modal decomposition

TitleParameter identification for the shallow water equation using modal decomposition
Publication TypeConference Papers
Year of Publication2007
AuthorsWut, Q., S. Amint, S. Munier, A. Bayen, X. Litrico, and G. Belaud
Conference NameDecision and Control, 2007 46th IEEE Conference on
Date PublishedDec
KeywordsCalifornia, Constraint optimization, Fluid flow measurement, Frequency domain analysis, Friction, friction coefficient, hydrological techniques, hyperbolic equations, Input variables, linear hyperbolic partial differential equations, linearized Saint-Venant equations, Matrix converters, modal decomposition, Nonlinear equations, nonlinear programming, optimization problem, parameter estimation, parameter identification, partial differential equations, periodic forcing, rivers, Sacramento-San-Joaquin Delta, shallow water equations, standard nonlinear programming, steady-state boundary conditions, tidal forcing, tides, transfer matrix

A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a spatially dependent transfer matrix relating the input variables to the output variables is obtained. It is shown that by considering a finite number of dominant oscillatory modes of the input, an accurate representation of the output can be obtained. This converts the original PDE constrained optimization problem to one without any constraints. The optimal parameters can be identified using standard nonlinear programming. The utility of the proposed approach is illustrated by considering a river reach in the Sacramento-San-Joaquin Delta, California, that is subjected to tidal forcing. The dynamics of the reach are modeled by linearized Saint-Venant equations. The available data is the flow variables measured upstream and downstream of the reach. The parameter identification problem is to estimate the average free-surface width, the bed slope, the friction coefficient and the steady-state boundary conditions. It is shown that the estimated model gives an accurate prediction of the flow variables at an intermediate location within the reach.